%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:56:17 EDT 2023

% Result   : Theorem 7.87s 8.62s
% Output   : Proof 7.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 19:05:53 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 7.87/8.62  
% 7.87/8.62  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 7.87/8.62  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.87/8.62  %-----------------------------------------------------
% 7.87/8.62  ncf(matrix, plain, [(512 ^ _63974) ^ [] : [empty(510 ^ [])], (514 ^ _63974) ^ [] : [-(ilf_type(510 ^ [], set_type))], (516 ^ _63974) ^ [] : [not_equal(identity_relation_of(510 ^ []), empty_set)], (96 ^ _63974) ^ [_67132, _67134, _67136, _67138] : [-(ordered_pair(_67138, _67134) = ordered_pair(_67136, _67132)), _67138 = _67136, _67134 = _67132], (106 ^ _63974) ^ [_67491, _67493, _67495, _67497] : [-(cross_product(_67497, _67493) = cross_product(_67495, _67491)), _67497 = _67495, _67493 = _67491], (116 ^ _63974) ^ [_67822, _67824] : [_67824 = _67822, -(subset_type(_67824) = subset_type(_67822))], (122 ^ _63974) ^ [_68040, _68042] : [_68042 = _68040, -(power_set(_68042) = power_set(_68040))], (128 ^ _63974) ^ [_68258, _68260] : [_68260 = _68258, -(member_type(_68260) = member_type(_68258))], (134 ^ _63974) ^ [_68456, _68458] : [_68458 = _68456, -(identity_relation_of(_68458) = identity_relation_of(_68456))], (2 ^ _63974) ^ [_64118] : [-(_64118 = _64118)], (4 ^ _63974) ^ [_64225, _64227] : [_64227 = _64225, -(_64225 = _64227)], (10 ^ _63974) ^ [_64429, _64431, _64433] : [-(_64433 = _64429), _64433 = _64431, _64431 = _64429], (20 ^ _63974) ^ [_64770, _64772, _64774, _64776] : [-(type(_64774, _64770)), type(_64776, _64772), _64776 = _64774, _64772 = _64770], (34 ^ _63974) ^ [_65186, _65188] : [-(relation_like(_65186)), _65188 = _65186, relation_like(_65188)], (44 ^ _63974) ^ [_65509, _65511, _65513, _65515] : [-(member(_65513, _65509)), member(_65515, _65511), _65515 = _65513, _65511 = _65509], (58 ^ _63974) ^ [_65925, _65927] : [-(empty(_65925)), _65927 = _65925, empty(_65927)], (68 ^ _63974) ^ [_66248, _66250, _66252, _66254] : [-(ilf_type(_66252, _66248)), ilf_type(_66254, _66250), _66254 = _66252, _66250 = _66248], (82 ^ _63974) ^ [_66672, _66674, _66676, _66678] : [-(not_equal(_66676, _66672)), not_equal(_66678, _66674), _66678 = _66676, _66674 = _66672], (140 ^ _63974) ^ [_68682] : [ilf_type(_68682, set_type), 143 ^ _63974 : [(144 ^ _63974) ^ [_68826] : [ilf_type(_68826, set_type), 147 ^ _63974 : [(148 ^ _63974) ^ [] : [member(_68826, _68682), -(member(ordered_pair(_68826, _68826), identity_relation_of(_68682)))], (154 ^ _63974) ^ [] : [member(ordered_pair(_68826, _68826), identity_relation_of(_68682)), -(member(_68826, _68682))]]]]], (160 ^ _63974) ^ [_69294] : [ilf_type(_69294, set_type), member(_69294, empty_set)], (166 ^ _63974) ^ [] : [-(empty(empty_set))], (168 ^ _63974) ^ [] : [-(type(empty_set, set_type))], (170 ^ _63974) ^ [_69591] : [ilf_type(_69591, set_type), 173 ^ _63974 : [(174 ^ _63974) ^ [_69752] : [ilf_type(_69752, set_type), 177 ^ _63974 : [(178 ^ _63974) ^ [_69908] : [ilf_type(_69908, set_type), 181 ^ _63974 : [(182 ^ _63974) ^ [] : [member(ordered_pair(_69752, _69908), identity_relation_of(_69591)), 185 ^ _63974 : [(186 ^ _63974) ^ [] : [-(member(_69752, _69591))], (188 ^ _63974) ^ [] : [-(_69752 = _69908)]]], (190 ^ _63974) ^ [] : [-(member(ordered_pair(_69752, _69908), identity_relation_of(_69591))), member(_69752, _69591), _69752 = _69908]]]]]]], (200 ^ _63974) ^ [_70563] : [ilf_type(_70563, set_type), -(ilf_type(identity_relation_of(_70563), binary_relation_type))], (206 ^ _63974) ^ [_70757] : [ilf_type(_70757, set_type), 209 ^ _63974 : [(210 ^ _63974) ^ [_70913] : [ilf_type(_70913, set_type), 213 ^ _63974 : [(234 ^ _63974) ^ [] : [-(_70757 = _70913), 236 ^ _63974 : [(237 ^ _63974) ^ [] : [-(ilf_type(235 ^ [_70757, _70913], set_type))], (239 ^ _63974) ^ [] : [240 ^ _63974 : [(241 ^ _63974) ^ [] : [-(member(235 ^ [_70757, _70913], _70757))], (243 ^ _63974) ^ [] : [member(235 ^ [_70757, _70913], _70913)]], 244 ^ _63974 : [(245 ^ _63974) ^ [] : [-(member(235 ^ [_70757, _70913], _70913))], (247 ^ _63974) ^ [] : [member(235 ^ [_70757, _70913], _70757)]]]]], (214 ^ _63974) ^ [] : [_70757 = _70913, 217 ^ _63974 : [(218 ^ _63974) ^ [_71172] : [ilf_type(_71172, set_type), 221 ^ _63974 : [(222 ^ _63974) ^ [] : [member(_71172, _70757), -(member(_71172, _70913))], (228 ^ _63974) ^ [] : [member(_71172, _70913), -(member(_71172, _70757))]]]]]]]]], (251 ^ _63974) ^ [_72175] : [ilf_type(_72175, set_type), 254 ^ _63974 : [(255 ^ _63974) ^ [_72316] : [ilf_type(_72316, set_type), 258 ^ _63974 : [(259 ^ _63974) ^ [] : [not_equal(_72175, _72316), _72175 = _72316], (265 ^ _63974) ^ [] : [-(_72175 = _72316), -(not_equal(_72175, _72316))]]]]], (271 ^ _63974) ^ [_72771] : [ilf_type(_72771, set_type), 274 ^ _63974 : [(285 ^ _63974) ^ [] : [287 ^ _63974 : [(288 ^ _63974) ^ [] : [-(ilf_type(286 ^ [_72771], set_type))], (290 ^ _63974) ^ [] : [-(member(286 ^ [_72771], _72771))]], -(empty(_72771))], (275 ^ _63974) ^ [] : [empty(_72771), 278 ^ _63974 : [(279 ^ _63974) ^ [_73014] : [ilf_type(_73014, set_type), member(_73014, _72771)]]]]], (294 ^ _63974) ^ [_73474] : [ilf_type(_73474, set_type), 297 ^ _63974 : [(298 ^ _63974) ^ [_73610] : [ilf_type(_73610, set_type), -(ilf_type(ordered_pair(_73474, _73610), set_type))]]], (304 ^ _63974) ^ [_73819] : [ilf_type(_73819, set_type), 307 ^ _63974 : [(308 ^ _63974) ^ [] : [ilf_type(_73819, binary_relation_type), 311 ^ _63974 : [(312 ^ _63974) ^ [] : [-(relation_like(_73819))], (314 ^ _63974) ^ [] : [-(ilf_type(_73819, set_type))]]], (316 ^ _63974) ^ [] : [-(ilf_type(_73819, binary_relation_type)), relation_like(_73819), ilf_type(_73819, set_type)]]], (327 ^ _63974) ^ [] : [-(ilf_type(325 ^ [], binary_relation_type))], (329 ^ _63974) ^ [_74488] : [ilf_type(_74488, set_type), 332 ^ _63974 : [(333 ^ _63974) ^ [] : [relation_like(_74488), 336 ^ _63974 : [(337 ^ _63974) ^ [_74760] : [ilf_type(_74760, set_type), member(_74760, _74488), 345 ^ _63974 : [(346 ^ _63974) ^ [] : [-(ilf_type(344 ^ [_74488, _74760], set_type))], (349 ^ _63974) ^ [] : [-(ilf_type(347 ^ [_74488, _74760], set_type))], (351 ^ _63974) ^ [] : [-(_74760 = ordered_pair(344 ^ [_74488, _74760], 347 ^ [_74488, _74760]))]]]]], (353 ^ _63974) ^ [] : [-(relation_like(_74488)), 355 ^ _63974 : [(356 ^ _63974) ^ [] : [-(ilf_type(354 ^ [_74488], set_type))], (358 ^ _63974) ^ [] : [-(member(354 ^ [_74488], _74488))], (360 ^ _63974) ^ [_75599] : [ilf_type(_75599, set_type), 363 ^ _63974 : [(364 ^ _63974) ^ [_75746] : [ilf_type(_75746, set_type), 354 ^ [_74488] = ordered_pair(_75599, _75746)]]]]]]], (372 ^ _63974) ^ [_76031] : [-(relation_like(_76031)), empty(_76031), ilf_type(_76031, set_type)], (382 ^ _63974) ^ [_76302] : [ilf_type(_76302, set_type), 385 ^ _63974 : [(386 ^ _63974) ^ [_76450] : [ilf_type(_76450, set_type), 389 ^ _63974 : [(390 ^ _63974) ^ [_76593] : [ilf_type(_76593, subset_type(cross_product(_76302, _76450))), -(relation_like(_76593))]]]]], (396 ^ _63974) ^ [_76817] : [ilf_type(_76817, set_type), 399 ^ _63974 : [(400 ^ _63974) ^ [_76953] : [ilf_type(_76953, set_type), -(ilf_type(cross_product(_76817, _76953), set_type))]]], (406 ^ _63974) ^ [_77162] : [ilf_type(_77162, set_type), 409 ^ _63974 : [(410 ^ _63974) ^ [_77307] : [ilf_type(_77307, set_type), 413 ^ _63974 : [(414 ^ _63974) ^ [] : [ilf_type(_77307, subset_type(_77162)), -(ilf_type(_77307, member_type(power_set(_77162))))], (420 ^ _63974) ^ [] : [ilf_type(_77307, member_type(power_set(_77162))), -(ilf_type(_77307, subset_type(_77162)))]]]]], (426 ^ _63974) ^ [_77778] : [ilf_type(_77778, set_type), -(ilf_type(429 ^ [_77778], subset_type(_77778)))], (433 ^ _63974) ^ [_78025] : [ilf_type(_78025, set_type), 436 ^ _63974 : [(437 ^ _63974) ^ [_78183] : [ilf_type(_78183, set_type), 440 ^ _63974 : [(455 ^ _63974) ^ [] : [457 ^ _63974 : [(458 ^ _63974) ^ [] : [-(ilf_type(456 ^ [_78025, _78183], set_type))], (460 ^ _63974) ^ [] : [-(member(456 ^ [_78025, _78183], _78025))], (462 ^ _63974) ^ [] : [member(456 ^ [_78025, _78183], _78183)]], -(member(_78025, power_set(_78183)))], (441 ^ _63974) ^ [] : [member(_78025, power_set(_78183)), 444 ^ _63974 : [(445 ^ _63974) ^ [_78446] : [ilf_type(_78446, set_type), member(_78446, _78025), -(member(_78446, _78183))]]]]]]], (466 ^ _63974) ^ [_79108] : [ilf_type(_79108, set_type), 469 ^ _63974 : [(470 ^ _63974) ^ [] : [empty(power_set(_79108))], (472 ^ _63974) ^ [] : [-(ilf_type(power_set(_79108), set_type))]]], (509 ^ _63974) ^ [_80375] : [-(ilf_type(_80375, set_type))], (498 ^ _63974) ^ [_80077] : [-(ilf_type(505 ^ [_80077], member_type(_80077))), -(empty(_80077)), ilf_type(_80077, set_type)], (474 ^ _63974) ^ [_79378] : [ilf_type(_79378, set_type), 477 ^ _63974 : [(478 ^ _63974) ^ [_79526] : [-(empty(_79526)), ilf_type(_79526, set_type), 485 ^ _63974 : [(486 ^ _63974) ^ [] : [ilf_type(_79378, member_type(_79526)), -(member(_79378, _79526))], (492 ^ _63974) ^ [] : [member(_79378, _79526), -(ilf_type(_79378, member_type(_79526)))]]]]]], input).
% 7.87/8.62  ncf('1',plain,[empty(510 ^ [])],start(512 ^ 0)).
% 7.87/8.62  ncf('1.1',plain,[-(empty(510 ^ [])), 288 : -(ilf_type(286 ^ [510 ^ []], set_type)), 285 : ilf_type(510 ^ [], set_type)],extension(271 ^ 1,bind([[_72771], [510 ^ []]]))).
% 7.87/8.62  ncf('1.1.1',plain,[ilf_type(286 ^ [510 ^ []], set_type), 298 : ilf_type(286 ^ [510 ^ []], set_type), 298 : -(ilf_type(ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), set_type))],extension(294 ^ 6,bind([[_73474, _73610], [286 ^ [510 ^ []], 286 ^ [510 ^ []]]]))).
% 7.87/8.62  ncf('1.1.1.1',plain,[-(ilf_type(286 ^ [510 ^ []], set_type))],reduction('1.1')).
% 7.87/8.62  ncf('1.1.1.2',plain,[ilf_type(ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), set_type), 222 : member(ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), identity_relation_of(510 ^ [])), 222 : -(member(ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), empty_set)), 218 : identity_relation_of(510 ^ []) = empty_set, 214 : ilf_type(empty_set, set_type), 210 : ilf_type(identity_relation_of(510 ^ []), set_type)],extension(206 ^ 9,bind([[_70757, _70913, _71172], [identity_relation_of(510 ^ []), empty_set, ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []])]]))).
% 7.87/8.62  ncf('1.1.1.2.1',plain,[-(member(ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), identity_relation_of(510 ^ []))), 148 : member(286 ^ [510 ^ []], 510 ^ []), 148 : ilf_type(286 ^ [510 ^ []], set_type), 144 : ilf_type(510 ^ [], set_type)],extension(140 ^ 18,bind([[_68682, _68826], [510 ^ [], 286 ^ [510 ^ []]]]))).
% 7.87/8.62  ncf('1.1.1.2.1.1',plain,[-(member(286 ^ [510 ^ []], 510 ^ []))],extension(290 ^ 23)).
% 7.87/8.62  ncf('1.1.1.2.1.2',plain,[-(ilf_type(286 ^ [510 ^ []], set_type))],lemmata('[1, 1].x')).
% 7.87/8.62  ncf('1.1.1.2.1.3',plain,[-(ilf_type(510 ^ [], set_type))],extension(514 ^ 19)).
% 7.87/8.62  ncf('1.1.1.2.2',plain,[member(ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), empty_set), -(member(ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), empty_set)), ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]) = ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), empty_set = empty_set],extension(44 ^ 18,bind([[_65509, _65511, _65513, _65515], [empty_set, empty_set, ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []])]]))).
% 7.87/8.62  ncf('1.1.1.2.2.1',plain,[member(ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), empty_set), ilf_type(ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), set_type)],extension(160 ^ 19,bind([[_69294], [ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []])]]))).
% 7.87/8.62  ncf('1.1.1.2.2.1.1',plain,[-(ilf_type(ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]), set_type))],reduction('1.1.1')).
% 7.87/8.62  ncf('1.1.1.2.2.2',plain,[-(ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]) = ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []]))],extension(2 ^ 19,bind([[_64118], [ordered_pair(286 ^ [510 ^ []], 286 ^ [510 ^ []])]]))).
% 7.87/8.62  ncf('1.1.1.2.2.3',plain,[-(empty_set = empty_set)],extension(2 ^ 19,bind([[_64118], [empty_set]]))).
% 7.87/8.62  ncf('1.1.1.2.3',plain,[-(identity_relation_of(510 ^ []) = empty_set), 265 : -(not_equal(identity_relation_of(510 ^ []), empty_set)), 265 : ilf_type(empty_set, set_type), 255 : ilf_type(identity_relation_of(510 ^ []), set_type)],extension(251 ^ 14,bind([[_72175, _72316], [identity_relation_of(510 ^ []), empty_set]]))).
% 7.87/8.62  ncf('1.1.1.2.3.1',plain,[not_equal(identity_relation_of(510 ^ []), empty_set)],extension(516 ^ 19)).
% 7.87/8.62  ncf('1.1.1.2.3.2',plain,[-(ilf_type(empty_set, set_type))],extension(509 ^ 17,bind([[_80375], [empty_set]]))).
% 7.87/8.62  ncf('1.1.1.2.3.3',plain,[-(ilf_type(identity_relation_of(510 ^ []), set_type))],extension(509 ^ 15,bind([[_80375], [identity_relation_of(510 ^ [])]]))).
% 7.87/8.62  ncf('1.1.1.2.4',plain,[-(ilf_type(empty_set, set_type))],extension(509 ^ 12,bind([[_80375], [empty_set]]))).
% 7.87/8.62  ncf('1.1.1.2.5',plain,[-(ilf_type(identity_relation_of(510 ^ []), set_type))],extension(509 ^ 10,bind([[_80375], [identity_relation_of(510 ^ [])]]))).
% 7.87/8.62  ncf('1.1.2',plain,[-(ilf_type(510 ^ [], set_type))],extension(514 ^ 2)).
% 7.87/8.62  %-----------------------------------------------------
% 7.87/8.62  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------